Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×D16 ⋊ C2 |
| Sylow | C7 ⋊ #2215 |
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^6104 conjugacy classes — view the full character table.
| maximal subgroup of | #13274433, #13274438, #13274443, … |
| maximal normal subgroup of | #13274433, #13274438, #13274443, … |
| maximal quotient of | #13267999, #13268050, #13268118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3989);